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Math · Advanced

Random Walks

Take a step left or right at the flip of a coin. Where do you end up? Random walks describe gamblers' fortunes, the jiggling of pollen in water, stock prices and diffusing molecules. Discover the square-root law, the gambler's ruin, and why a drunk person always finds home but a drunk bird might not.

7 lessons~35 min0/7 complete
1

Walking at Random

The square-root law.

  1. The Drunkard’s WalkHow far do you get?
  2. Gambler’s RuinWhy the house always wins
2

Walks in Nature

Diffusion and dimension.

  1. Brownian MotionJiggling pollen and diffusion
  2. Lost in Three DimensionsPólya’s theorem
3

Hidden Laws of Walks

Leads, ballots and walkers that solve equations.

  1. Who’s in the Lead?The arcsine law and the ballot theorem
  2. Walkers That Solve EquationsRandom walks and steady heat
  3. Seven ShufflesHow random is a shuffled deck?